A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices

@inproceedings{Mehta2004ASF,
  title={A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices},
  author={Vikram Bhagvandas Mehta and Wilberd van der Kallen},
  year={2004}
}
We exhibit a nice Frobenius splitting σ on G× b where b is the Lie algebra of the Borel group B of upper triangular matrices in the general linear group G = Gln. What is nice about it, is that it descends along familiar maps and specializes to familiar subvarieties in a manner that is useful for the study of the singularities of closures of conjugacy classes of nilpotent n by n matrices. In particular, we show that these closures are simultaneously Frobenius split, are normal, and have rational… CONTINUE READING

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